ABSTRACT

In the application of high-dimensional data classification, several attempts have been made to achieve variable selection by replacing the ${\ell }_2$-penalty with other penalties for the support vector machine (SVM). However, these high-dimensional SVM methods usually do not take into account the special structure among covariates (features). In this article, we consider a classification problem, where the covariates are ordered in some meaningful way, and the number of covariates p can be much larger than the sample size n. We propose a structured sparse SVM to tackle this type of problems, which combines the non-convex penalty and cubic spline estimation procedure (i.e. penalizing second-order derivatives of the coefficients) to the SVM. From a theoretical point of view, the proposed method satisfies the local oracle property. Simulations show that the method works effectively both in feature selection and classification accuracy. A real application is conducted to illustrate the benefits of the method.

摘要

在高维数据分类的应用中，已经进行了多种尝试，以通过替换变量来实现变量选择。 ${\ell }_2$-支持向量机（SVM）的其他惩罚。但是，这些高维SVM方法通常不考虑协变量（特征）之间的特殊结构。在本文中，我们考虑一个分类问题，其中协变量以某种有意义的方式排序，并且协变量p的数量可能远大于样本大小n。我们提出了一种结构化的稀疏SVM来解决此类问题，该方法将非凸罚分和三次样条估计程序（即惩罚系数的二阶导数）组合到了SVM中。从理论上讲，所提出的方法满足了本地的oracle属性。仿真表明，该方法在特征选择和分类精度上均有效。进行了实际应用以说明该方法的好处。